Coefficient of Friction Question.

In summary, the parcel slips up the inclined plane, the normal reaction is 18N, and the coefficient of friction is 0.18.
  • #1
_Mayday_
808
0
Hey, I would like to check that my working for the following question is along the right lines. I have an exam this coming Wednesday and there are a few really common questions that I think I should do some work on. As always any help is much appreciated! :smile:

The Question

A parcel of weight 10N lies on a rough plane inclined at an angle of 30 degrees to the horizontal. A horizontal force of magnitude P Newtons acts on the parcel as shown in the attachment (Bottom of post). The parcel is in equilibrium and on the point of slipping up the plane. The normal reaction of the plane on the parcel is 18N. The coefficient of friction between the parcel and the plane is [itex]\mu[/itex]. Find:

(a) The value of P

(b) The value of [itex]\mu[/itex]

The horizontal force is removed.

(c) Determine whether or not the parcel moves.

My Attempt

(a) Resolve perpendicular to the plane:

[itex]18 - 10\cos30 - P\sin 30[/itex]

[itex]18 = 10\cos30 + P\sin 30[/itex]

[itex]18 - 5\sqrt3 = \frac{P}{2}[/itex]

[itex]2(18 - 5\sqrt3) = P = 18.7N[/itex]

(b) Resolve along the plane.

[itex]F + 10\sin30 = 18.7\cos30[/itex]

[itex]5F = 16.20[/itex]

[itex]F = 3.24[/itex]

Now I just plug in the answer from (a) with this one from (b)

[itex]F=\mu R[/itex]

[itex]3.24 = 18\mu[/itex]

[itex]\mu = 0.18[/itex]

I am still working on (c) but could someone please have a look at how I am doing so far. I may have skipped a few steps, but I am just using the fact that when resolving perpendicular you can always use cos, and whenever you resolve parallel you can use sin, when dealing with vectors int his course on an inclined plane.

Thank you.

_Mayday_
 

Attachments

  • Mechanics Diagram.bmp
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  • #2
I didn't check your arithmetic, but your method is correct.
 
  • #3
I think you have made an arithmetic mistake in part (b) - the second line of working for (b) is inconsistent with the first line.
 
  • #4
For (c), consider the maximum value which friction can take, remembering that now that P has been removed, the normal reaction will change. Compare this to the component of weight down the slope.
 
  • #5
nokia8650 said:
I think you have made an arithmetic mistake in part (b) - the second line of working for (b) is inconsistent with the first line.
nokia8650 is correct--you made an arithmetic mistake in part (b).
 
  • #6
[itex]F + 10\sin30 = 18.7\cos30 [/itex]
[itex]5F = 16.20[/itex]

Ah right!

[itex]F + 10\sin30 = 18.7\cos30[/itex]
[itex]F + 5 = 16.20[/itex]
[itex]F = 11.20[/itex]

[itex]\mu = 0.62[/itex]

Thanks for that, silly mistake. I'll have a look at your advice in a minute or two nokia. Thank you both Nokia and Doc.

_Mayday_ :approve:
 

What is the coefficient of friction?

The coefficient of friction is a measurement of the amount of resistance between two surfaces when one surface moves over the other. It is a unitless value and can range from 0 (no friction) to 1 (high friction).

How is the coefficient of friction calculated?

The coefficient of friction is calculated by dividing the force of friction by the normal force. The force of friction is the force required to keep an object moving at a constant speed over another surface, and the normal force is the force exerted by the surface on the object in a direction perpendicular to the surface.

What factors can affect the coefficient of friction?

The coefficient of friction can be affected by several factors, including the nature of the surfaces in contact, the roughness of the surfaces, the amount of force pressing the surfaces together, and the presence of any lubricants or contaminants.

How is the coefficient of friction important in everyday life?

The coefficient of friction is important in everyday life because it affects how objects move and interact with each other. It is essential in the design of machinery and structures, as well as in sports and other activities where friction plays a role.

What are some applications of the coefficient of friction in science?

The coefficient of friction is used in various fields of science, including physics, engineering, and materials science. It is essential in understanding and predicting the behavior of objects in motion, as well as in the design and development of new materials and technologies.

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